How to generate all possible vectors where each element can take one of two values

Given vectors a and b both of length N, I want to generate the 2^N vectors for which element i is either a[i] or b[i]. For example, if a=[1,2,3] and b=[4,5,6], then I want to generate

C =

1 2 3

1 2 6

1 5 3

1 5 6

4 2 3

4 2 6

4 5 3

4 5 6

I can do this with the following code

N = length(a);

M = ff2n(N);

Mc = abs(M-1);

C = a.*Mc + b.*M;

but I'm wondering if there is a better way to accomplish this, possibly not requiring ff2n which is not part of standard MATLAB installation? Is there a way to use nchoosek or permute or something like that?

Answer 1

[Paul]

a = [1 2 3];
b = [4 5 6];

n = numel(a);
C = mat2cell([a; b],2,ones(1,n));
[D{1:n}] = ndgrid(C{:});
E = sortrows(cell2mat(cellfun(@(x) x(:),D,'UniformOutput',false)))

E = 8×3

1 2 3 1 2 6 1 5 3 1 5 6 4 2 3 4 2 6 4 5 3 4 5 6

Answer 2

[Torsten]

Generate all possible combinations of 0 and 1:

m = 3;
justRows = dec2bin(0:2^m-1)-'0'

Now replace the 0's by a(i) and the 1 by b(i).

[Kevin Galloway]

Thanks, Torsten; I appreciate your thoughts on this. Just to clarify, your code essentially replaces ff2n in my code; is that correct? Part of my question was to see if there was a more straightforward way to solve my problem without creating the binary matrix, then assigning a(i) and b(i), etc. I.e. is there a function that would accomplish all of this without the intermediate steps of developing the binary matrix? If not, I do appreciate your answer since it works without the ff2n toolbox function.

[Torsten]

You can use "allcomb" available here:

https://de.mathworks.com/matlabcentral/fileexchange/10064-allcomb-varargin

a=[1,2,3];
b=[4,5,6];
A = [a;b];
result = allcomb(A(:,1),A(:,2),A(:,3))

[Kevin Galloway]

Thanks, Torsten. This is a nice function, and an efficient way of accomplishing my task. Much appreciated!